An Explicit Solution for Progress Curve Analysis in Systems Characterized by Endogenous Substrate Production

The Lambert W function was used to explicitly relate substrate concentration S , to time t , and the kinetic parameters V m , K m , and R in the modified Michaelis–Menten equation that accounts for endogenous substrate production. The applicability of this explicit formulation for kinetic parameter estimation by progress curve analysis was demonstrated using a combination of synthetic and experimental substrate depletion data. Synthetic substrate depletion data were generated using S 0 values of 1, 2, and 3 μM and V m , K m , and R values of 1.0 μM h −1 , 1.0 μM, and 0.1 μM h −1 , respectively, and contained 5% normally distributed error. Experimental data were obtained from two previously published studies on hydrogen depletion in four experimental systems. In all instances, experimental data were well described by the explicit solution presented in this study. Differential equation solution and iterative S estimation are eliminated with the explicit solution approach, thereby simplifying progress curve analysis in systems characterized by endogenous substrate production.